no. G8
Équations aux dérivées partielles
Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation
Kfoury, Perla1 ; Le Coz, Stefan1 ; Tsai, Tai-Peng2
1 Institut de Mathématiques de Toulouse ; UMR5219, Université de Toulouse ; CNRS, UPS IMT, F-31062 Toulouse Cedex 9,France
2 Department of Mathematics, University of British Columbia, Vancouver BC, Canada V6T 1Z2
Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 867-892.

For the double power one dimensional nonlinear Schrödinger equation, we establish a complete classification of the stability or instability of standing waves with positive frequencies. In particular, we fill out the gaps left open by previous studies. Stability or instability follows from the analysis of the slope criterion of Grillakis, Shatah and Strauss. The main new ingredients in our approach are a reformulation of the slope and the explicit calculation of the slope value in the zero-frequency case. Our theoretical results are complemented with numerical experiments.

Reçu le :
Révisé le :
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DOI : 10.5802/crmath.351
Classification : 35Q55, 35B35
Mots clés : nonlinear Schrödinger equation, double power nonlinearity, standing waves, stability, orbital stability
Kfoury, Perla 1 ; Le Coz, Stefan 1 ; Tsai, Tai-Peng 2

1 Institut de Mathématiques de Toulouse ; UMR5219, Université de Toulouse ; CNRS, UPS IMT, F-31062 Toulouse Cedex 9,France
2 Department of Mathematics, University of British Columbia, Vancouver BC, Canada V6T 1Z2 
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     title = {Analysis of stability and instability for standing waves of the double power one dimensional nonlinear {Schr\"odinger} equation},
     journal = {Comptes Rendus. Math\'ematique},
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Kfoury, Perla; Le Coz, Stefan; Tsai, Tai-Peng. Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation. Comptes Rendus. Mathématique, Tome 360 (2022) no. G8, pp. 867-892. doi : 10.5802/crmath.351. http://www.numdam.org/articles/10.5802/crmath.351/

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